## Integers and a deck of cards

One of the easiest ways to practice integers is with a deck of cards. Take out all the face cards except the aces, which count as ones. Working in pairs is ideal, but groups of 3 or 4 will work. Below are some ideas for card games, but please be advised that card games are a waste of time if your students are struggling with integers. If a student can’t add 2 + (-7), they’re not suddenly going to be able to add them just because the numbers are now on a card. There are more efficient methods for guiding below level students to understanding integers.

These games are only good for students who have a good grasp of integers, but just need to work on speed. Plus they make a great end of the year or “just before Christmas break and we don’t want to do anything” activity. Or if you are tutoring a struggling student one on one and are actually going to play with the student yourself.

WAR
The winner is the one who ends up with the deck of cards or the one who has the most cards when time is called.

One Operation

Deal the cards evenly between the players. Each player lays down two cards. They must add (or subtract or multiply, depending on your instructions) and whoever has the highest value wins. (You could modify to lowest value). For advanced students, change the number of cards laid down to 3 (or 4) instead of just 2.

All Operations
This time, students may use any operation to get the highest value. For example, a 9 of hearts and a 3 of spades added together gives a -6, subtracted gives a +12 or -12, multiplied gives a -27 and divided gives a -3 (division never wins). The best option in this case is to subtract for the +12. The other student has an 8 of clubs and a 2 of spades. Multiplying them gives a value of +16, so the second student wins. (Students must inform each other which operation they have chosen. If the second student had chosen subtraction, for instance, then the first student would win the cards).

TRIPLES
The winner is the one who no longer has any cards in their hand, or whoever has the most triples when time is called.

All Operations
Each player gets seven cards, the rest are face down in a stack to draw from. They can set down triple sets when added, subtracted, multiplied or divided.
For example, a 6 of hearts and a 2 of spades could equal -4, 8, -8, or -3 (answers must be 10 or below since the highest value card is 10). So the student could set down the 6 of hearts, 2 of spades and an 8 of spades as a valid set.
To start the game, the first student lays down all the triples in his hand. He then draws a card to see if he can make a triple with the new card. If he can’t, it’s the other student’s turn. They continue taking turns until all cards are drawn.
As the students are playing, I’ll walk around the room and ask them to explain their triples.

25
The ideal size for this game is small groups of 3 or 4. Deal the whole deck of cards to the players. Players should keep their own cards face down in a stack. The first player picks up a card from her stack and lays it face up in the middle. Let’s say she shows an 8 of hearts (-8). She must say “pass,” because the total thus far is not 25. The next player then reveals a card from his stack, and lays it down next to the first player’s card. In this example, let’s say he has a 9 of spades (+9). The total so far would be +1, so the second player must now say “pass.” This keeps going until a player reveals a card that makes the total = 25, at which point the player who laid the card down would shout “25.” If a player says “pass” when the sum is 25, the first of the other players to shout “25″ wins.
It’s a good idea for students to keep a running sum written on a sheet of paper, as this can get pretty long. Or to make the game easier, simply make the target number lower.

TARGET
For this game, it’s best to leave the face cards in. Black face cards are 10, red face cards are -10. Each player gets dealt 8 cards, the rest of the cards are face down in a stack to draw from. Flip the top card over, that becomes the target number. The first player draws a card and then sets down any pairs of cards that when added or subtracted equals the target number. Then it’s the next player’s turn. This goes around until a student runs out of cards or all the cards have been drawn. The player that runs out of cards first is the winner.

## T-Chart Adding and Subtracting Integers

I’ve found a method that the students have grasped fairly quickly for performing integer operations. It’s called the T-chart, and it works very well. The student creates a two column chart, one column is labeled with a + and the other with a -. Then the student places the values in their appropriate column. If the numbers are already in the same column, they add. If they are in different columns, they move the smaller of the two and subtract.

For example:
3 + -11

+ | -
3 | 11 (To represent 3 positives and 11 negatives)

They move the 3 under the 11 like so:
+ | -
__| 11
__| 3
(Ignore the underscores, this site won’t leave the space on the web page)
Since they moved the number, they subtract and get 8. Since 8 is in the negative column, the answer is -8.

Another example:
-3 + -9

+ | -
__| 3
__| 9
Since the two numbers are already in the same column, they add to get 12, and since it’s in the negative column, the answer is -12.

Hope this helps!

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## How Do You Teach Adding and Subtracting Integers?

I am teaching a lower level class this year for the first time, and am very surprised at some of my students’ inability to grasp the concept of integers. I had to have them use + and – to visually show integer addition. 3 + -4 would be expressed as +++ and – - – -. Since each pair cancels out, there is one negative left over, and therefore the answer is negative one. We did this for several days, and then moved on to bigger numbers. I thought that the students could visualize 23 – 31 as drawing 23 positives and 31 negatives. Since there are more negative signs, I thought they would be able to understand that there would be some negative signs left over, and that the answer had to come from subtracting the two, which would be -8. But they won’t take the time to think the problem through, nor do they want to take the time to draw so many positive and negative signs to find the correct answer the long way.

At any rate, I do not want to teach the rules (2 positives = positive, 2 negatives = negative, opposite signs = take the absolute value, whichever is greater, that is the sign of the answer then subtract the two). I know that is what they’re doing when they draw positive and negative signs, but if I teach it explicitly in that manner, then the students will confuse those rules with the rules of multiplying and dividing integers when we study that section. Does anyone have any good ideas? I did try the money analogy: -3 + 5 means you owe three dollars, but you have five dollars. Since you always pay off your debt, then you have to give 3 of your dollars to pay off your debt, which leaves you 2 dollars (having money is a positive thing). Likewise, -6 + 2 means you owe six dollars, but you have 2, so you give your two away and you still owe 4 dollars (owing money is a negative thing). Does anyone have any better ideas?

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